The Red Sox needed me like the Sahara needed more sand. I was like the insurance policy for the insurance policy.

“We’re going to call you up once the Triple-A playoffs finish,” I was told. It was 2011, the Red Sox had been arguably the best team in baseball for the first five months of the season and had entered September with a robust nine-game lead in the playoff race. It wasn’t a question of making the playoffs — rather, all anyone wondered was if they could clinch home-field advantage for the entire postseason.

But when August slipped into September, the ice started thinning beneath their feet. By the time I arrived at Fenway on Sept. 13, the big-league club had just returned to Boston after going 1-6 on the most recent road trip. Their September record was a woeful 2-9. The all-too-familiar taste of concern-bordering-on-panic wafted through the clubhouse as I walked through the doors with my gear and found my locker. I remember thinking to myself,...